Hi there,
These capacitors are filter ones and need to be placed in various spots on the board, near voltage inputs, outputs, IC power pins and other place, so they filter the noise on the Vcc line across the board, so that's why they are many and connected on main voltage.
1n5422 diodes (Schottky diode 40V 2A) are used to protect the ICs from reverse input voltage on their Vin pins, as they allow current to flow in one direction. You can use any Schottky diode with same characteristics.
Welcome to our community,
Mike

This is a popular ESR meter across the web and we also have a revision of it published here:
http://www.electronics-lab.com/project/advanced-lc-meter/
Regarding your questions on the first message, let's see if someone who has build it can help out.

I came across 2 builds of this power supply with lot's of info on the process and tuning of it.
http://diyfan.blogspot.com/2012/02/adjustable-lab-power-supply.html
http://www.paulvdiyblogs.net/2015/05/tuning-030v-dc-with-03a-psu-diy-kit.html
Worth checking these websites.

Hi Tintin,
You have done excellent work building this power supply and your experience is valuable for all other members. I encourage you to translate the PDF in English so anyone can benefit from it. Looking forward seeing your measurements and thoughts building this PSU.

Hi and welcome to our community,
To help you out we will need more information about your connections and software used. A clear schematic will help us locate any issue and your code will provide additional insight.

Hi,
To achieve what you would like you need a programmable timer to be able to set the ON-OFF time at high precision. I don't know if you can find such timer in the market, as most timers are rated about 16A and are weekly programmable. What possibly you could do is to use a timer to set the ON time and keep the OFF time manually. In this case a timer like:
http://www.electronics-lab.com/project/2-digit-99-seconds-timer/
http://www.electronics-lab.com/project/1-to-100-seconds-timer/
may help.